Introduction of Heatmap for Applications in Water Distribution Network

ABSTRACT
In water distribution network (WDN) domain, pressure sensitivity matrix (or so-called Jacobian matrix) is used to represent the unit changes of pressure at different locations under disturbances (e.g., variation in pipe roughness and nodal demand). Considering it as a sub-component for other main computations, previous studies have simply used the matrix in a step for (1) WDN reliability quantification and for (2) sensor/meter placement. Although it contains useful information of hydraulic response between different locations over the network, few efforts have been devoted to visualizing the sensitivity matrix (to be more useful and interpretable), investigating different types of the matrices, and providing the comprehensive guidance in usage. To that end, this study proposes the use of “Heatmap”, a visualized version of the pressure sensitivity matrix. Total four different pressure gradient matrices are suggested and converted to “Heatmap”: pressure sensitivity under pipe breakage, diameter change, demand changes, and pipe roughness coefficient (e.g., Hazen-Williams) changes. While the proposed methods are applied to two benchmark networks (Hanoi and Mays) and a real WDN (KL), the results obtained are summarized into a full comprehensive guidance on (1) how to construct the Heatmap (normalization and coloring/scaling), (2) how to interpret the resulting Heatmap, and (3) which type of map to use for different WDN problems (critical pipe-line selection, pipe parallelization).

ACKNOWLEDGEMENT
This work was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No. 2020R1C1C1006481).